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Category: Arithmetic

n-1-30-n-2-1-A-n-1-15-2n-2-30n-224-B-n-1-15-2n-2-30n-225-C-n-1-15-2n-2-30n-226-D-n-1-15-2n-2-30n-227-E-n-

Question Number 17767 by Joel577 last updated on 10/Jul/17 $$\underset{{n}\:=\:\mathrm{1}} {\overset{\mathrm{30}} {\sum}}\left({n}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:=\: \\ $$$$\left(\mathrm{A}\right)\:\underset{{n}\:=\:\mathrm{1}} {\overset{\mathrm{15}} {\sum}}\left(\mathrm{2}{n}^{\mathrm{2}} \:+\:\mathrm{30}{n}\:+\:\mathrm{224}\right) \\ $$$$\left(\mathrm{B}\right)\:\underset{{n}\:=\:\mathrm{1}} {\overset{\mathrm{15}} {\sum}}\left(\mathrm{2}{n}^{\mathrm{2}} \:+\:\mathrm{30}{n}\:+\:\mathrm{225}\right) \\ $$$$\left(\mathrm{C}\right)\:\underset{{n}\:=\:\mathrm{1}}…

Question-148780

Question Number 148780 by Jonathanwaweh last updated on 31/Jul/21 Answered by Kamel last updated on 31/Jul/21 $$ \\ $$$$\Omega=\underset{{n}=\mathrm{2}} {\overset{+\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } ={e}^{\underset{{n}=\mathrm{2}} {\overset{+\infty}…

Question-83242

Question Number 83242 by peter frank last updated on 29/Feb/20 Commented by john santu last updated on 29/Feb/20 $$\left(\mathrm{4b}\right)\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{r}\left(\mathrm{r}+\mathrm{1}\right)\:=\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{r}^{\mathrm{2}} \:+\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}}…

Question-148753

Question Number 148753 by Jonathanwaweh last updated on 30/Jul/21 Answered by mathmax by abdo last updated on 31/Jul/21 $$\mathrm{A}_{\mathrm{n}} =\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{n}} \:\mathrm{e}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\right)^{\mathrm{k}^{\mathrm{2}} } \:\Rightarrow\mathrm{A}_{\mathrm{n}}…

If-a-0-n-1-2a-1-x-2-n-2-4n-5-x-16-0-is-a-perfect-square-such-that-n-Z-what-is-the-value-of-x-n-

Question Number 83188 by john santu last updated on 28/Feb/20 $$\mathrm{If}\:\underset{\mathrm{a}\:=\:\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\left(\mathrm{2a}+\mathrm{1}\right)\mathrm{x}^{\mathrm{2}} +\left(\mathrm{n}^{\mathrm{2}} +\mathrm{4n}−\mathrm{5}\right)\mathrm{x}+\mathrm{16} \\ $$$$=\:\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{n}\:\in\:\mathbb{Z}^{+} \:.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{x}\:+\mathrm{n}\:?\: \\ $$ Answered…